digital design m morris mano 5th edition, Lecture notes of Computer Vision

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Solution to Problems

Chapter 4 & 5

“Digital Design” by M. Morris Mano

ECE 223 Fall 2005

Amir Khatibzadeh

aakhatib@optimal.vlsi.uwaterloo.ca

4-23 A^1 A^0 E

D^0

= (A

+A 1

+E’)’=A 0

’A 1

’E 0

D^1

= (A

+A 1

’+E’)’=A 0

’A 1

E 0

D^2

= (A

’+A 1

+E’) =A 0

A 10

’E

D^3

= (A

’+A 1

’+E’) =A 0

A 10

E

4-28^ F= x (y + y’) z + x’y’z’ =^1

Σ^ (0, 5, 7)

F= x y’z’ + x’y (z + z’) =^2

Σ^ (2, 3, 4)

F= x’y’z + x y (z + z’) =^3

Σ^ (1, 6, 7)

3 x 8Decoder

F^1 F^2 F^3

x y z

(^221202)

8 x 1MUX 8 x 1MUX

S^0 S^1 S^201234567 S^0 S^1 S^201234567

S^0 S^1 S^2 S^3

2 x 1MUX

Y

S 0 1

4 x 1MUX

S^0 S^2 I^0 I^1 I^2 I^3

Y^

F

A B C

A B C D

F

AB=00F=D AB=01F=C’D’=(C+D)’AB=10F=CD AB=11F=

D

D

CP^

C

R=(D+C’)’= D’C

S=D.C

Q Q’

C

S=(D’+C’)’= D.C

D^

Q Q’

R=D’C

5-1 (a)

5-1 (b)

5-4^ P

N

Q(t+1)

Q(t)

Q’(t)

5-4(a)

P^

N^

Q(t) Q(t+1)

5-4(b)

Q(t)

Q(t+1)

P

N

X

X

X^

X^

5-4(c)

5-4(d)

Connect P and N togetherQ(t+1)= PQ’+NQ

1 1

1

1

P

N

Q(t)

x

CP

A B

y

z

D^ Q Q’^ D

x’y+xA

5-6 (a)

PresentStateAB^00011011

NextStateAB^01100000

FF TA^0111

InputsTB^1101

TA = A + BTB = A’ + BRepeated Sequence

PresentStateAB^00000000010101011010101011111111

Inputsxy^00011011000110110001101100011011

NextStateAB^10001101010110111010001010101010

Outputz^0000100000011001

5-10 (b)

FF InputsJ K^ A^ A

J B

KB

1^ 5-10 (c)

1 1

1

1

1

1

1

1

1

1

B

x

00

xy

AB 0001 1110

A^ A (t+1)=Ax’+ Bx + Ay+ A’B’y’

1

1

1

1

1 00

xy

AB 0001 1110^ B (t+1)=A’B’x+ A’B’(x’+y)